# Integers and Net Worth

### Objective

Students will be able to:

- Represent net worth using an integer number sentence.
- Represent net worth using a vertical number line.
- Transform net worth statements into integer number sentences.
- Perform integer addition.
- Hypothesize changes in assets and liabilities that result in no change to net worth.

### Concepts

Using number sentences to represent net worth students explore addition of integers into assets, liabilities & net worth.

### Resources

### Procedure

Warm-Up

Show students Slide 2 from the Resource Slides. Tell students that the homes in the pictures are owned by two different families. Ask students which family they think has the most money, or wealth. (Most students will answer the one on the right.) Tell students that in this lesson we will explore the concept of “net worth” and how it is calculated. Explain that having a big house or possessions does not always reflect a person’s net worth.

Show Slide 3. Define the terms “assets” and “liabilities”. Ask students to identify some examples of assets that families may have. (Answers may vary but may include a home, car, savings, or jewelry.) Tell students that monetary value is not the same as personal value. For example, they may love their old sneakers, but they probably cannot sell them to someone else for very much money. Ask students to share about a possession they have that has high personal value to them, but little value to others. Explain that items often have a high personal value to us but little, if any, monetary value to others. Ask students to identify some examples of liabilities that families may have. (Answers may vary but may include student loans, home mortgages, credit card debt, or car loans.)

Show Slide 4. Tell students that these young people are known for having a high net worth. Ask students if they recognize the names of any of these individuals. (Answers will vary.) Tell students that you found the net worth for some people under 30. Ask if they know any of these actors or athletes. (Answers will vary.) Ask students if they think the average person under 30 has a net worth that is higher or lower than Chloe Kim’s. (Some students will say yes; some will say no). Ask students to explain their answers. (Answers may vary but may include fame brings money.)

Show Slide 5. Have students respond to the questions about Chloe Kim’s net worth: Where do you think Chloe Kim’s money might be? (Answers may vary, but students are likely to say the bank.) Do you think she has any “debts” or “liabilities?” (Most should answer yes.) What sort of “liabilities” might Chloe Kim have? (Answers may vary but students might say cars loans, house loans.) What assets do you think she might have? (Answers may vary, but students are likely to say gold medal, savings account, checking account, house, car, jewelry).

Modeling

Tell students that their comparison of Ms. Kim’s assets and liabilities would be much more accurate if they had actual numbers to use. Show Slides 6 and 7 and tell the students that a net worth statement specifies a person’s assets and liabilities in current dollars to calculate their net worth. Briefly use the assets and liabilities suggested by the students to create a net worth statement for Chloe Kim. You need not focus on totals yet.

Explain that net worth net worth can be expressed using integer number sentences. Share examples of integers from Chloe Kim’s net worth statement. Represent liabilities as negative integers and assets as positive integers. Tell the students that liabilities are represented as negative numbers because they are quantities owed to others.

Show Slide 8. Tell students that Sasha is a teenager with a credit card. Share with students that Sasha’s family co-signed to secure a credit card for her. Also share that Sasha has a part-time job. Tell students that they are looking at a net worth statement for Sasha. Ask students what they notice about Sasha’s net worth statement. (Answers will vary, but students are likely to notice that assets and liabilities have the same total. Some students will notice that the total net worth for Sasha is currently zero.) Ask students which integers are used to find Sasha’s net worth. (800, 1,000, -1,800.) Remind students that liabilities are negative numbers because they are quantities owed to others. Have students write a number sentence showing Sasha’s net worth. (Answers will vary, but students are likely to write 800 + 1,000 + -1,800 = 0; or 800 + 1,000 + 1,800 = 3,600).

Show Slide 9 to be sure students represent her assets, liabilities, and recognize the zero pair.

Show Slide 10. Explain to students how they can use integers to show changes in Sasha’s net worth using number sentence and a number line.

Show Slide 11. Note that Sasha’s net worth statement has changed. Ask students what has changed. (The coin collection has been added as an asset.) Tell the students that Sasha’s aunt gave her a valuable coin collection. Ask the students whether the coin collection positively or negatively affects Sasha’s net worth. (It positively affects, or increases, her net worth). Tell the students that the coin collection is worth $500. Have students recalculate her net worth using a number sentence.

Show Slide 12. Review the changes in Sasha’s net worth. Point out that a person’s net worth changes constantly. As they earn income or pay off their debt, their net worth reflects those changes.

Show Slide 13. Have students draw new number line showing the change in Sasha’s net worth (including the coin collection). (The assets should now exceed the liabilities by $500).

Show Slide 14. Tell students that Sasha has decided to go to college and has taken out a student loan. Tell the students that you do not know the value of the loan Sasha took out. Ask the student how the loan impacts Sasha’s net worth. (The loan is a promise to pay and so Sasha’s net worth goes down). Ask the students if Sasha’s net worth can still be positive. (Answers will vary, but If Sasha has borrowed less than 500 dollars her net worth is still positive). Ask the students to represent Sasha’s net worth if the loan is for $1,000. Focus on zero pairs rather than adding using sequential addends (800 + 1,000 + 500 + -1,800 + -1000 = -500; Sasha now has a net worth of -$500.). Review student answers and respond to any questions.

Group Activity

Show Slide 15. Put students in pairs or small groups and distribute copies of Sam Loves Sneakers! All Kinds!. Review the directions and give students 15 minutes to complete the worksheet. (Note: You may also want to have groups prepare a poster, slide, or other similar illustration to show what is happening to Sam’s net worth. Encourage students to be creative with their presentation. You may select students to present to illustrate different models or use a gallery walk with students making sticky note comments on posters.). Show Slide 16 to review the activity.

Prior to doing the individual activity, review slides 17 and 18 asking the students to share their insights from the group activity. Remind students that integers are positive and negative whole numbers and zero. Review the process for adding integers and creating a number line.

Individual Activity

Distribute copies of Personal Net Worth Activity. Review the instructions with students, encouraging them to use “pretend” information to complete the activity. Remind students of the importance of protecting personal information while still practicing the process of finding their net worth. (Answers will vary. If you choose, you could assign them categories and dollar amounts.)

### Assessment

Distribute copies of Using Integers to Find Net Worth Assessment to review student learning. If time allows, you may want to review student answers before they submit their answers.